computer exercise

Computer Exercise Problem: (a) Generate two discrete-time (with 10 Hz sampling rate and 100 time points) sample functions of two random sinusoids X(t) =2.6sin(4.2t + ) and Y(t) = 2.1 sin(4.4t + ), respectively, where U(0, 4) and U(-,) are independent. Save the functions as data files m10_3x. dat and m10_y. dat, respectively. (b) Let Z(t) = X(t) + Y(t). Read in the two data records from the two data files, add the corresponding terms to yield a data record for Z(t) and save it as m10_3z.dat. (c) Use pwelch to estimate and plot the power spectrum of Z(t). (d) Repeat (a), (b), and (c) using 10 Hz sampling rate and 1000 time points. Adjust sequence length. (e) Discuss the frequency resolutions of the two power spectra of Z(t) based on your results. Matlab code: clear clc t=0:0.1:100; m=4*pi*rand(1,1); X=2.6*sin(4.2*pi*t+m); N=1001; fw = fopen(m10_3x.dat, w); fwrite(fw, X, double); fclose(fw); fr=fopen(m10_3x.dat,r); x=fread(fr,N,double); fclose(fr); n=-pi+2*pi*rand(1,1); Y=2.1*sin(4.4*pi*t+n); fw = fopen(m10_3y.dat, w); fwrite(fw, Y, double); fclose(fw); fr=fopen(m10_3y.dat,r); y=fread(fr,N,double); fclose(fr); z=x+y; fw = fopen(m10_3z.dat, w); fwrite(fw, z, double); fclose(fw); fz=pwelch(z); len=length(fz); figure(1); plot(1:len, fz) xlim(40,80); t=0:0.1:1000; m=4*pi*rand(1,1); X=2.6*sin(4.2*pi*t+m); N=10001; fw = fopen(m10_3x.dat, w); fwrite(fw, X, double); fclose(fw); fr=fopen(m10_3x.dat,r); x=fread(fr,N,double); fclose(fr); n=-pi+2*pi*rand(1,1); Y=2.1*sin(4.4*pi*t+n); fw = fopen(m10_3y.dat, w); fwrite(fw, Y, double); fclose(fw); fr=fopen(m10_3y.dat,r); y=fread(fr,N,double); fclose(fr); z=x+y; fw = fopen(m10_3z.dat, w); fwrite(fw, z, double); fclose(fw); fz=pwelch(z); len=length(fz); figure(2); plot(1:len, fz) xlim(800,950); Results: The